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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Invariant and simulation analysis to the time fractional Abrahams-Tsuneto reaction diffusion system
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Invariant and simulation analysis to the time fractional Abrahams-Tsuneto reaction diffusion system

机译：不变和仿真分析到分数亚伯拉罕 - TSUNETO反应扩散系统

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摘要

In this work, symmetry analysis and numerical approximations to the time fractional Abrahams- Tsuneto reaction diffusion system (ATRDS) are discussed. We obtain point symmetries, similarity variables, similarity transformation and reduce the time-fractional ATRDS to time-fractional systems of ordinary differential equations. In the reduced equation, the derivative is in Erdelyi-Kober sense. The numerical analysis and simulations are performed using a powerful iterative method called residual power series (RPS) method. The validity and correctness of the RPS method is illustrated by analyzing the approximate solutions graphically and comparing the approximates solutions with exact solutions in tables 1 and 2. The given examples in this paper confirm that the RPS can be used as an alternative for finding approximate solutions for fractional equations. The generalization of ATRDS to time fractional derivative was not reported previously, to the best of our knowledge it is reported for the first time in this research.
机译：在该工作中，讨论了对称分析和数值近似于分数亚伯拉姆 - Tsuneto反应扩散系统（ATRD）的数值分析和数值近似。我们获得点对称，相似度变量，相似性变换并减少常微分方程的时间分数系统的时间分数亚峰。在降低的方程中，衍生物是Erdelyi-kober的感觉。使用称为残余功率系列（RPS）方法的强大迭代方法进行数值分析和仿真。 RPS方法的有效性和正确性是通过以图形方式分析和比较表1和2中具有精确解的近似解的近似解。本文给出的实施例证实，RPS可以用作查找近似解决方案的替代方案用于分数方程。迄今未提前报告过时的ATRDS与时间分数衍生物的泛化，这是我们在本研究中首次报告的。

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